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assignment :-
Simple instrument and its usage
You need a thick art paper to prepare a model
project. On the other hand, the stationary
store you know is not even opening due to
Covid- 19 pandemic. The only stationary
store that is open now has a bad reputation in
the locality for being dishonest. But you are
somewhat compelled now to buy paper from
him. The shopkeeper is claiming that the
value of the paper which he supplied you is
160 gm/m2
.
The size of per sheet of modeling paper is
65cm X 75cm. You decided that you will
verify the shopkeeper. The measuring tape
you have at home cannot measure anything
that is less than 2 cm. And also, the digital
balance which you have in your house for
measuring the mass of the cooking
ingredients does not record any mass bellow
20gm. This means that if you want to
measure the mass of an 8 grams object
accurately, you have to take 5 objects. So
that their combined mass is 40 grams which
is a multiple of 20 grams. You have no scope
to use any other instrument.
a) What is the dimension of the unit by which
the value of the paper is being measured? (1)
b) What will be its unit if it is measured in
Kilogram? (2)
c) What is the least number of papers you
need to buy to be sure about this matter?
Give logic in favour of your calculation. (3)
d) If the value of each paper written on the
packet as (120±0.5) gm/m2
, it means that the
value is actually in between 119.5 to120.5
units. Here the final error is 0.5 units.
Determine the accuracy of your measured
value? (4)
Answers:-
(A)
The value of paper is measured in units
-2
Dimensions ML
(B)
The following units are found in units of paper quality in kilograms-
(We know),
1000g = 1kg-3
1g = 10 kg
10-3kg
So, 160-
2
m
. . . -3 2
= 160 times 10-kg m
No. c
Here, 1 paper length = 75 cm and width = 65 cm
Thus, the length of 2 sheets = 75 + 75 = 150 cm = 1.5 m
Width of 2 papers = 65 + 65 = 130 cm = 1.3 m
Thus, the area of the paper = 1.5×1.3 m²
= 1.95 m
Again, according to the shopkeeper,
Paper mass = 160 g / m
Then, the mass of 1m² = 160 g
:. Now, the mass of 1.95m² = 160×1.95g
= 312 grams
Here, 312×1 = 312, which is not divisible by 20.
312×2 = 624, which is not divisible by 20.
312 × 3 = 936, which is not divisible by 20.
312×4 = 1248, which is not divisible by 20.
312×5 = 1560, which is not divisible by 20.
Then, the total paper required = 4×5 = 20 (ans)
D-
= Here
Given value = 120 ° + • 5gm / m2
The value of the final error is 0.5 units
We know
Relative error = final error /
Value or measured value
0-5 / 120
= 4.167X10-3 cubes
Percentage calculation – (4167 × 10-3 cubes × 100)%
= 0.4167%
Error value – 0.416%
Accurate- (100-0.4167)%
99.58%
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